Sinn Féin's Mr Seán Crowe has topped the poll in Dublin South West, marking a significant increase in support across the State.
Mr Crowe was deemed elected when he exceeded the quota after the first count. He received 7,466 first-preference votes.
In the key constituency of Kerry North, there were indications from early tallies of the Tralee count that Mr Martin Ferris was performing strongly and could top the poll.
Ballot boxes from his native Ardfert and from Fenit showed him ahead of former tánaiste Mr Dick Spring, Fine Gael's Mr Jimmy Deenihan and Fianna Fail's two candidates Mr Tom McEllistrim and Mr Dan Kiely.
As the first ballot boxes from Tralee were opened, there were reports that Fianna Fáil's Mr Tom McEllistrim may be ahead of Mr Spring.
Sinn Féin's Aenghus O'Snodaigh also appears to be polling well in Dublin South Central, where support for Fine Gael's Mr Gay Mitchell seems to have collapsed.
Mr Arthur Morgan in Louth is thought may oust Mr Michael Bell of the Labour party.
